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x^2 - 2x[x] +x - k= 0 , find real k, so that it has >=2 non-negative roots

Source: Vietnam MO 1979 P5

July 28, 2018
algebraInteger Partequation

Problem Statement

Find all real numbers kk such that x2−2x[x]+x−k=0x^2 - 2 x [x] + x - k = 0 has at least two non-negative roots.
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